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**Unformatted text preview: **1 Chapter 5: Circular Motion Uniform Circular Motion Radial Acceleration Banked and Unbanked Curves Circular Orbits Nonuniform Circular Motion Tangential and Angular Acceleration Artificial Gravity 2 3 Examples of circular motion Wheels of cars Propellers on airplanes Hard disks . 4 5.1 Uniform Circular Motion Here, v 0. The direction of v is changing. If v 0, then a 0. The net force cannot be zero. Consider an object moving in a circular path of radius r at constant speed. x y v v v v 5 Conclusion: to move in a circular path, an object must have a nonzero net force acting on it. 6 7 is the angular position. Angular displacement: i f - = Note: angles measured CW are negative and angles measured CCW are positive. is measured in radians. 2 radians = 360 =1 revolution x y i f To simplify description: angles instead of distances 8 The average and instantaneous angular velocities are: t t t = = av lim and is measured in rads/sec. 9 An object moves along a circular path of radius r; what is its average speed? av av time total distance total r t r t r v = = = = Also, r v = (instantaneous values). x y i f r 10 x y i f r arclength = s = r r s = is a ratio of two lengths; it is a dimensionless ratio! Question 1 An object is in uniform circular motion. Which of the following statements is true? A) Velocity = constant B) Speed = constant C) Acceleration = constant Question 2 A CD makes one complete revolution every tenth of a second. The angular velocity of point 4 is: A) the same as for pt 1. B) twice that of pt 2. C) half that of pt 2. D) 1/4 that of pt 1. E) four times that of pt 1. 13 The time it takes to go one time around a closed path is called the period (T). T r v 2 time total distance total av = = Comparing to v=r : f T 2 2 = = f is called the frequency , the number of revolutions (or cycles) per second. 14 15 16 5.2 Centripetal Acceleration The velocity of a particle is tangent to its path. For an object moving in uniform circular motion, the acceleration is radially inward. 17 The magnitude of the radial acceleration v r r v a r = = = 2 2 18 19 Example (text problem 5.14): The rotor is an amusement park ride where people stand against the inside of a cylinder....

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